A simple analytical form of the Thomas-Fermi screening function and of Firsov's atomic interaction potential

The Thomas-Fermi screening function ∅( x ) is shown to be accurately described by the expression 317 × exp(-6.62 x 1/4 ) in the range 0.3 < x < 16. The consequent form of the Thomas-Fermi electron density distribution is derived, and Firsov's atomic interaction potential is shown to have the form E = B exp(-α r 1/4 ), where B and α are constants of known Z dependence and r is the internuclear distance. It is also suggested that a potential of the type E' = A' exp(- k'r 1/3 ) gives a better representation of the interaction potential over a wider range of energies and distances, and explicit values of A' and k' are given for copper-copper interactions. However, the Z dependence of A' and k' is not obvious.